where “0” denotes present values and “eq” denotes the time of matter-radiation equality; “RH” signals the end of reheating, and “end” means the end of inflation, i.e. when \(\epsilon _H=1\) . For any comoving scale \(k\) , one obtains for the no. of efolds at horizon crossing [1]}, [2]}, [3]}:
\(N(k)= 56.01 - \ln \frac{k}{k_*} + \ln \frac{a_{end}}{a_{RH}} + \ln \frac{\rho _{RH}^{1/4}}{10^{16} {\rm GeV}} + \frac{1}{2}\ln \frac{\rho _k}{\rho _{RH}} \,. \) 
